Logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverse of exponential functions. If y = b^x, then x = log_b(y).

Front

How do you convert an exponential equation to logarithmic form?

Back

To convert b^c = a to logarithmic form, write it as log_b(a) = c.

Front

What is the logarithmic form of 5^2 = 25?

Back

log_5(25) = 2.

Front

Evaluate: log_9(3)

Back

1/2.

Front

What is the value of log_5(1)?

Back

0, because 5^0 = 1.

Front

What is the value of log_b(b)?

Back

1, because b^1 = b.

Front

If log_2(x) = 3, what is x?

Back

x = 2^3 = 8.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.